Certain navigational applications have a need for high precision sensors. For example, MEMS vibratory sensors may be capable of providing high precision measurements. MEMS vibratory sensors may consist of one or more proof masses connected to a substrate through flexible suspensions (flexures) such that the MEMS sensor has two resonant modes. A velocity induced by driving the proof masses along the first resonant mode (drive mode) produces a Coriolis force on the second mode (sense mode) when the substrate is rotated. The resulting displacement of the sense mode at the drive frequency provides an output of the sensor, which is a measure of the rotation rate. Alternatively, the output of a force rebalance control loop that nulls the sense mode displacement may also provide a measure of the rotation rate.
A common sensor output error is bias or zero-rate offset. A bias error occurs when the sensor output is non-zero when there is no substrate rotation. Systems may be able to compensate for the bias error if the bias is repeatable due to environmental conditions, such as temperature, that vary in a repeatable manner. However, there may be some level of error that is non-compensatable such as bias due to hysteresis or stress relaxation in materials, non-zero thermal time constants, aging of electronics components, or other factors.
One cause of non-compensatable bias error is due to mechanical coupling of the sensor to a substrate. Imperfect fabrication of the sensor, which may include imperfect coupling of the sensor and substrate, may cause the driven motion of the drive mode to be asymmetric, producing a net force and/or moment on the substrate. The imbalanced force or moment exerted on the substrate can produce motion in structures external to the sensor. This external motion can in turn exert a force and/or moment on the sense mode of the sensor, producing a bias signal at the sensor output. If the external motion and/or the mechanical coupling of the substrate to the sensor has non-repeatable variation over changes in temperature, then the compensated bias of the sensor may not account for the non-repeatable variation.
Typical two-mass MEMS sensors, known to one having skill in the art, have substantial non-compensatable bias because the sense mode motion has net angular momentum. Thus, sense mode motion can be produced by rotational vibration of the substrate even if the gyroscope is perfectly fabricated.